Introduction

Latitudinal migration is a widespread phenomenon across animal taxa. There is a wide range of migration strategies employed by species, particularly regarding when and how they migrate.
Extent (range, distance) and fine-scale timing of latitudinal migration are well studied, but mostly put in context of vegetation phenology in breeding range (Briedis et al. 2020) or environmental conditions in wintering range (Saino et al. 2004; Gordo et al. 2005) or physiology [e.g., Gomez et al 2016, Zurell et al. 2018]. There has also been particular attention on how extent and timing of migration might be affected by climate change (Rushing et al. 2020).
Species migrating to equatorial/tropical latitudes, where environmental cues such as photoperiod are poor predictors of seasons, tend to rely more on their internal circannual clocks (Wikelski et al. 2007; Liedvogel et al. 2011; Åkesson et al. 2017). This aspect of migratory restlessness driven by species-specific internal clocks has been referred to as Zugunruhe (Gwinner 1967; Gwinner 1986).
However, a basic aspect of migration timing that has remained understudied is migration synchronicity. How quickly or slowly do species complete the occupation or evacuation (arrival or departure) of their wintering ranges? What determines which of these strategies a species employs? Why do some species spend longer occupying or vacating their nonbreeding range, while their close relatives spend much shorter times for these?
There is a great diversity in species-specific strategies employed in this regard, with some species seeming to arrive across their broad wintering range all at once and some others occupying their southern limits months after the northern limits.
We know that such relationships between wintering latitude and migration timing are important (and more so than breeding latitude) (Hagan et al. 1991; Schmaljohann 2018).
Migration synchronicity is thus an emergent species-level property that has implications for all geographies occupied by the species. e.g., for certain species, India hosts their entire global population in winter (Blyth’s Reed Warbler, Greenish Warbler)—global ecological (and conservation) significance.
Yet, much of this understanding of synchronicity remains anecodtal, unquantified, and without ecological context, particularly in countries like India. Such a macroecological understanding is difficult to obtain from studies of individual movement patterns, such as tracking studies.
India occupies a large area and forms the wintering range for a large number of bird species (cite SoIB maps?) (also multiple flyways). In addition, the unique biogeography of the peninsula (funnelling/tapering down to lower latitudes before ending with the ocean) offers a unique opportunity to test such macroecological hypotheses regarding the link between migration synchronicity and wintering latitudes. (This part can be supported by a figure: map of India for two wintering months, latitudes binned and coloured based on density of no. of wintering/all species.)

What we know

At the finer scale of individual migrating birds, migration speed is closely linked to flight speed and/or stopover duration (rest, fuel) (Schmaljohann 2018). Translated to macroecological context, migration synchronicity can be associated with intrinsic species-specific factors as well as external factors like environmental and landscape features. The major internal factors possibly affecting synchronicity are species’ morphological traits (affecting flight speed capability, such as dispersal ability, body size?), migration distance (Winger et al. 2024), and urgency of migration (related to within- and across-season differences in programming of internal clocks). On the other hand, external factors refer to the biogeomorphology of migration routes and wintering ranges, which influences food availability, interspecific competition, etc. and therefore influences how conducive various latitudes are to the fitness of the birds.

There is evidence that the latter is more important (Lindström 2003; Nilsson et al. 2013; Schmaljohann 2018), even at the macroecological scale (La Sorte et al. 2016). That is, external factors influencing aspects of foraging/fuelling are more important than intrinsic morphological or programmed factors like Zugunruhe. In India, this might be especially true for species taking the northwest vs Himalayan migration routes. In terms of both food availability and competition, the arid northwest region of India might be very conducive during the post-monsoon period (coinciding with arrival of winter migrants), due to the sudden burst in food availability coupled with lower competitive pressure due to lower local species richness. Thus, many species taking this route may spend longer coming down to reach the southern limit of their wintering range.

We test these multiple theories using our dataset, with the following predictions (simple illustrative graphs can be created later):

If synchronicity is linked to species morphology, synchronicity increases with increasing flight capability (dispersal ability/HWI, body mass, ?)
If synchronicity is determined by migration distance (geographical separation of breeding and non-breeding ranges), it:
1. increases with greater wintering latitudinal breadth (or with more southern minimum wintering latitude) [this is an extension of below]
2. increases with greater migration distance (Hagan et al. 1991; Winger et al. 2024) [not sure if we want to test this]
If synchronicity is driven by urgency of migration, it:
1. increases with later migration start day (Lack 1950; Hagan et al. 1991)
2. is greater during departures (spring migration) than in arrivals (autumn migration) (Nilsson et al. 2013; Schmaljohann 2018; Winger et al. 2024)
If synchronicity is related to biogeomorphological factors, synchronicity of arrivals (autumn migration) is lesser for species using the northwest route of entry and greater for those crossing the Himalaya, whereas synchronicity of departures (spring migration) is not notably different between the two.
Null?

Exploration (methods)

For high-res versions of images, go here.

Metrics

Migration timing:
- True arrival/departure dates, not absolute (stragglers)
- Synchronicity
Wintering latitude:
- Minimum
- Extent/breadth/range
- Median (probably not useful, other two capture enough info)

Investigating arrival and departure timings & synchronicity

After all our selection and filtering criteria for wintering species of interest (giving 90 species), and after filtering data for each species to its wintering latitudinal range (removing latitudes where not purely wintering), we now start the analysis.

Using quantiles (assuming 95%), we determine “true” arrival and departure dates for each species per latitude. For a preliminary visualisation of patterns across species, we visualise this latitudinal trend of arrival (blue) & departure (red) times for all species:

Figure 1: True arrival and departure timings of our wintering species, using the quantile method.

Figure 2: True arrival and departure timings of our wintering species, using the quantile method.

We now calculate metrics for migration timings, such as first northern/southern arrival & departure, and synchronicity which is our primary metric of interest. We describe synchronicity using two (presumably) orthogonal angles: slope (quickness of migration) and tightness (uniformity) across latitudes. (Correlation R² cannot be used for the measure of tightness, since for high slope values, R² becomes low.)

Here are the synchronicity measures (SYNC.SLOPE & SYNC.TIGHT) for a set of illustrative species, followed by updated plots for the same species.

## # A tibble: 50 × 6
##    COMMON.NAME               DATE.TYPE   SLOPE    SE SYNC.SLOPE SYNC.TIGHT
##    <chr>                     <fct>       <dbl> <dbl>      <dbl>      <dbl>
##  1 Cinereous Vulture         DEP        6.21   0.921  -1.60         0.0827
##  2 Bar-tailed Godwit         DEP        3.89   2.60   -1.19        -0.956 
##  3 Brown-breasted Flycatcher DEP        2.47   0.479  -0.795        0.737 
##  4 Black Redstart            DEP        2.21   0.292  -0.696        1.23  
##  5 Blyth's Reed Warbler      DEP        1.86   0.213  -0.548        1.55  
##  6 Red-breasted Flycatcher   DEP        1.53   0.312  -0.373        1.16  
##  7 Lesser Whitethroat        DEP        1.50   0.462  -0.361        0.771 
##  8 Common Chiffchaff         DEP        1.46   0.410  -0.332        0.891 
##  9 Siberian Stonechat        DEP        1.39   0.246  -0.293        1.40  
## 10 Bar-headed Goose          DEP        1.26   0.283  -0.203        1.26  
## 11 Taiga Flycatcher          DEP        0.988  0.300   0.00665      1.21  
## 12 Eurasian Wigeon           DEP        0.795  0.344   0.197        1.07  
## 13 Brown-headed Gull         DEP       -0.766  0.472   0.229        0.750 
## 14 Brown Shrike              DEP        0.519  0.282   0.570        1.27  
## 15 Tufted Duck               DEP        0.511  0.447   0.584        0.806 
## 16 Spotted Redshank          DEP        0.504  0.327   0.595        1.12  
## 17 Greenish Warbler          DEP       -0.459  0.362   0.677        1.02  
## 18 Gray Wagtail              DEP        0.425  0.253   0.745        1.38  
## 19 Green Warbler             DEP        0.363  0.467   0.883        0.762 
## 20 Common Buzzard            DEP       -0.272  0.880   1.13         0.128 
## 21 Greater Spotted Eagle     DEP        0.245  0.254   1.23         1.37  
## 22 Sykes's Warbler           DEP        0.147  0.847   1.67         0.166 
## 23 Western Yellow Wagtail    DEP        0.0612 0.241   2.44         1.42  
## 24 Booted Eagle              DEP       -0.0444 0.250   2.72         1.39  
## 25 Pallid Harrier            DEP        0.0227 0.334   3.31         1.10  
## 26 Blyth's Reed Warbler      ARR       -3.33   0.459  -1.06         0.778 
## 27 Cinereous Vulture         ARR       -2.39   2.38   -0.766       -0.866 
## 28 Green Warbler             ARR       -1.78   0.270  -0.510        1.31  
## 29 Brown-breasted Flycatcher ARR       -1.78   1.02   -0.506       -0.0229
## 30 Western Yellow Wagtail    ARR       -1.73   0.204  -0.481        1.59  
## 31 Pallid Harrier            ARR       -1.62   0.240  -0.423        1.43  
## 32 Sykes's Warbler           ARR       -1.51   0.984  -0.362        0.0157
## 33 Eurasian Wigeon           ARR       -1.35   0.272  -0.266        1.30  
## 34 Common Chiffchaff         ARR       -1.22   0.440  -0.176        0.821 
## 35 Brown-headed Gull         ARR       -1.04   0.533  -0.0368       0.630 
## 36 Bar-tailed Godwit         ARR       -0.997  0.958  -0.000733     0.0428
## 37 Greenish Warbler          ARR       -0.980  0.280   0.0143       1.27  
## 38 Booted Eagle              ARR       -0.976  0.209   0.0177       1.57  
## 39 Brown Shrike              ARR       -0.732  0.160   0.270        1.83  
## 40 Taiga Flycatcher          ARR       -0.722  0.250   0.281        1.39  
## 41 Siberian Stonechat        ARR       -0.705  0.182   0.302        1.70  
## 42 Tufted Duck               ARR       -0.700  0.527   0.308        0.640 
## 43 Red-breasted Flycatcher   ARR       -0.642  0.248   0.384        1.39  
## 44 Lesser Whitethroat        ARR       -0.610  0.255   0.429        1.36  
## 45 Spotted Redshank          ARR        0.552  1.02    0.516       -0.0168
## 46 Common Buzzard            ARR        0.480  0.335   0.637        1.09  
## 47 Black Redstart            ARR       -0.409  0.172   0.779        1.76  
## 48 Gray Wagtail              ARR        0.342  0.209   0.934        1.57  
## 49 Bar-headed Goose          ARR       -0.129  0.146   1.79         1.92  
## 50 Greater Spotted Eagle     ARR        0.0515 0.332   2.59         1.10

Figure 3: Set of illustrative species arranged in order of synchronicity of arrival/departure.

Figure 4: Set of illustrative species arranged in order of synchronicity of arrival/departure.

All our species can be visualised as occupying a 2-D space governed by the two measures of synchronicity. Based on their occupancy of this space, we can classify their overall synchronicity.

Figure 5: 2D space of synchronicity measures of our species.

Now will try to combine the two variables into a single index of synchronicity. Relative weights are obtained from PCA of the two variables, and the index (SYNC.IND) is a linear combination of the two. New values and updated graphs below.

## # A tibble: 50 × 5
##    COMMON.NAME               DATE.TYPE SYNC.SLOPE SYNC.TIGHT SYNC.IND
##    <chr>                     <fct>          <dbl>      <dbl>    <dbl>
##  1 Bar-tailed Godwit         DEP        -1.19        -0.956  -1.12   
##  2 Cinereous Vulture         DEP        -1.60         0.0827 -1.08   
##  3 Brown-breasted Flycatcher DEP        -0.795        0.737  -0.320  
##  4 Black Redstart            DEP        -0.696        1.23   -0.0982 
##  5 Lesser Whitethroat        DEP        -0.361        0.771  -0.00962
##  6 Common Chiffchaff         DEP        -0.332        0.891   0.0472 
##  7 Blyth's Reed Warbler      DEP        -0.548        1.55    0.102  
##  8 Red-breasted Flycatcher   DEP        -0.373        1.16    0.103  
##  9 Siberian Stonechat        DEP        -0.293        1.40    0.233  
## 10 Bar-headed Goose          DEP        -0.203        1.26    0.252  
## 11 Taiga Flycatcher          DEP         0.00665      1.21    0.378  
## 12 Brown-headed Gull         DEP         0.229        0.750   0.391  
## 13 Eurasian Wigeon           DEP         0.197        1.07    0.466  
## 14 Tufted Duck               DEP         0.584        0.806   0.653  
## 15 Spotted Redshank          DEP         0.595        1.12    0.757  
## 16 Greenish Warbler          DEP         0.677        1.02    0.782  
## 17 Brown Shrike              DEP         0.570        1.27    0.786  
## 18 Common Buzzard            DEP         1.13         0.128   0.822  
## 19 Green Warbler             DEP         0.883        0.762   0.846  
## 20 Gray Wagtail              DEP         0.745        1.38    0.940  
## 21 Sykes's Warbler           DEP         1.67         0.166   1.21   
## 22 Greater Spotted Eagle     DEP         1.23         1.37    1.27   
## 23 Western Yellow Wagtail    DEP         2.44         1.42    2.13   
## 24 Booted Eagle              DEP         2.72         1.39    2.31   
## 25 Pallid Harrier            DEP         3.31         1.10    2.62   
## 26 Cinereous Vulture         ARR        -0.766       -0.866  -0.797  
## 27 Blyth's Reed Warbler      ARR        -1.06         0.778  -0.487  
## 28 Brown-breasted Flycatcher ARR        -0.506       -0.0229 -0.357  
## 29 Sykes's Warbler           ARR        -0.362        0.0157 -0.245  
## 30 Bar-tailed Godwit         ARR        -0.000733     0.0428  0.0127 
## 31 Green Warbler             ARR        -0.510        1.31    0.0545 
## 32 Common Chiffchaff         ARR        -0.176        0.821   0.133  
## 33 Pallid Harrier            ARR        -0.423        1.43    0.151  
## 34 Western Yellow Wagtail    ARR        -0.481        1.59    0.160  
## 35 Brown-headed Gull         ARR        -0.0368       0.630   0.170  
## 36 Eurasian Wigeon           ARR        -0.266        1.30    0.220  
## 37 Spotted Redshank          ARR         0.516       -0.0168  0.351  
## 38 Greenish Warbler          ARR         0.0143       1.27    0.405  
## 39 Tufted Duck               ARR         0.308        0.640   0.411  
## 40 Booted Eagle              ARR         0.0177       1.57    0.498  
## 41 Taiga Flycatcher          ARR         0.281        1.39    0.624  
## 42 Red-breasted Flycatcher   ARR         0.384        1.39    0.697  
## 43 Lesser Whitethroat        ARR         0.429        1.36    0.719  
## 44 Siberian Stonechat        ARR         0.302        1.70    0.736  
## 45 Brown Shrike              ARR         0.270        1.83    0.754  
## 46 Common Buzzard            ARR         0.637        1.09    0.779  
## 47 Black Redstart            ARR         0.779        1.76    1.08   
## 48 Gray Wagtail              ARR         0.934        1.57    1.13   
## 49 Bar-headed Goose          ARR         1.79         1.92    1.83   
## 50 Greater Spotted Eagle     ARR         2.59         1.10    2.13

Figure 6: Species arranged in order of combination of two synchronicity measures.

Figure 7: Species arranged in order of combination of two synchronicity measures.

Clearly, there is still some finetuning to be done with the “quickness” metric, i.e., derived from slope. For the most synchronous species with little difference between them, the values are drastically different. Also need to figure out how to appropriately weight the two so that high togetherness is prioritised.

Further try ordinations to understand what factors (wintering, migrating) determine synchronicity of species.

Finalise synchronicity

On discussing with AV, we realised that the second aspect, “tightness” is better viewed as noise rather than information. Even if it appears to have ecological meaning, this is only true for high tightness values and here the information is mostly just from the first metric. So, instead of trying to combine the two aspects, better to ignore species with tightness lower than some threshold value. Consider that low tightness can either be just noise in data, or lack of a strong north-south migration signal in the species, and we can’t tease apart the two (and not of interest in this study; though might still be an orthogonal aspect of synchronicity). So, changes applied:

Set threshold for variability (tightness) along slope, exclude species above this from our main regression tests with latitude
With all species (including those excluded above), we divide synchronicity into N bins (think X axis of Fig. 5) and within each bin show how variability (signal) can range from low to high. e.g., highly staggered species can range from BRW (very strong migration signal) to CiVu (less strong signal); very synchronous species can range from BHGo to SpRedshank.
So now our measure of synchronicity is much simplified: there is only one metric, and that too can be simply the slope from the LM (without any transformations).
- LM seems the best bet here; I did try GLM Poisson but the slope there is not the information we want
- Also, LM estimates with and without scaling the DAY.MY to start from 0 (for each species and arrival/departure combo) were the same, so leave it unscaled. See below.

## # A tibble: 5 × 8
##   COMMON.NAME             DATE.TYPE LM.SLOPE LM.SE SCALED.LM.SLOPE SCALED.LM.SE GLM.SLOPE GLM.SE
##   <chr>                   <fct>        <dbl> <dbl>           <dbl>        <dbl>     <dbl>  <dbl>
## 1 Black-capped Kingfisher ARR        -2.11    2.87         -2.11           2.87     0.979   1.01
## 2 Black-naped Oriole      ARR         2.78    1.47          2.78           1.47     1.03    1.00
## 3 Black-throated Thrush   ARR        -3.67    1.39         -3.67           1.39     0.876   1.03
## 4 Common Pochard          ARR         0.0714  1.06          0.0714         1.06     1.00    1.00
## 5 Eurasian Griffon        ARR        -0.514   2.05         -0.514          2.05     0.942   1.08

Arranging in order of new synchronicity index (slope of LM):

## # A tibble: 50 × 4
##    COMMON.NAME               DATE.TYPE SYNC.IND    SE
##    <chr>                     <fct>        <dbl> <dbl>
##  1 Brown-headed Gull         DEP        -0.766  0.472
##  2 Greenish Warbler          DEP        -0.459  0.362
##  3 Common Buzzard            DEP        -0.272  0.880
##  4 Booted Eagle              DEP        -0.0444 0.250
##  5 Pallid Harrier            DEP         0.0227 0.334
##  6 Western Yellow Wagtail    DEP         0.0612 0.241
##  7 Sykes's Warbler           DEP         0.147  0.847
##  8 Greater Spotted Eagle     DEP         0.245  0.254
##  9 Green Warbler             DEP         0.363  0.467
## 10 Gray Wagtail              DEP         0.425  0.253
## 11 Spotted Redshank          DEP         0.504  0.327
## 12 Tufted Duck               DEP         0.511  0.447
## 13 Brown Shrike              DEP         0.519  0.282
## 14 Eurasian Wigeon           DEP         0.795  0.344
## 15 Taiga Flycatcher          DEP         0.988  0.300
## 16 Bar-headed Goose          DEP         1.26   0.283
## 17 Siberian Stonechat        DEP         1.39   0.246
## 18 Common Chiffchaff         DEP         1.46   0.410
## 19 Lesser Whitethroat        DEP         1.50   0.462
## 20 Red-breasted Flycatcher   DEP         1.53   0.312
## 21 Blyth's Reed Warbler      DEP         1.86   0.213
## 22 Black Redstart            DEP         2.21   0.292
## 23 Brown-breasted Flycatcher DEP         2.47   0.479
## 24 Bar-tailed Godwit         DEP         3.89   2.60 
## 25 Cinereous Vulture         DEP         6.21   0.921
## 26 Blyth's Reed Warbler      ARR        -3.33   0.459
## 27 Cinereous Vulture         ARR        -2.39   2.38 
## 28 Green Warbler             ARR        -1.78   0.270
## 29 Brown-breasted Flycatcher ARR        -1.78   1.02 
## 30 Western Yellow Wagtail    ARR        -1.73   0.204
## 31 Pallid Harrier            ARR        -1.62   0.240
## 32 Sykes's Warbler           ARR        -1.51   0.984
## 33 Eurasian Wigeon           ARR        -1.35   0.272
## 34 Common Chiffchaff         ARR        -1.22   0.440
## 35 Brown-headed Gull         ARR        -1.04   0.533
## 36 Bar-tailed Godwit         ARR        -0.997  0.958
## 37 Greenish Warbler          ARR        -0.980  0.280
## 38 Booted Eagle              ARR        -0.976  0.209
## 39 Brown Shrike              ARR        -0.732  0.160
## 40 Taiga Flycatcher          ARR        -0.722  0.250
## 41 Siberian Stonechat        ARR        -0.705  0.182
## 42 Tufted Duck               ARR        -0.700  0.527
## 43 Red-breasted Flycatcher   ARR        -0.642  0.248
## 44 Lesser Whitethroat        ARR        -0.610  0.255
## 45 Black Redstart            ARR        -0.409  0.172
## 46 Bar-headed Goose          ARR        -0.129  0.146
## 47 Greater Spotted Eagle     ARR         0.0515 0.332
## 48 Gray Wagtail              ARR         0.342  0.209
## 49 Common Buzzard            ARR         0.480  0.335
## 50 Spotted Redshank          ARR         0.552  1.02

Figure 8: Species arranged in order of synchronicity (slope).

Figure 9: Species arranged in order of synchronicity (slope).

Determining threshold cutoff for variability (tightness)

This is not very straightforward. Here is a summary of some select species and various measures of theirs (R-squared, residual standard error, degrees of freedom, F statistic, root mean square error, mean absolute error, coefficient of variation).

## # A tibble: 50 × 11
##    COMMON.NAME               DATE.TYPE   SLOPE    SE       R2   RSE    DF   F.STAT  RMSE   MAE    CV
##    <chr>                     <fct>       <dbl> <dbl>    <dbl> <dbl> <int>    <dbl> <dbl> <dbl> <dbl>
##  1 Brown-headed Gull         DEP       -0.766  0.472 0.141    13.2     16  2.63    12.5   9.69  1.32
##  2 Greenish Warbler          DEP       -0.459  0.362 0.0745   10.8     20  1.61    10.3   8.83  1.19
##  3 Common Buzzard            DEP       -0.272  0.880 0.00679  21.2     14  0.0958  19.9  14.1   1.45
##  4 Booted Eagle              DEP       -0.0444 0.250 0.00174   6.45    18  0.0314   6.12  4.95  1.27
##  5 Pallid Harrier            DEP        0.0227 0.334 0.000256  8.96    18  0.00460  8.50  7.00  1.25
##  6 Western Yellow Wagtail    DEP        0.0612 0.241 0.00293   8.50    22  0.0646   8.14  6.13  1.36
##  7 Sykes's Warbler           DEP        0.147  0.847 0.00200  18.5     15  0.0301  17.3  13.1   1.37
##  8 Greater Spotted Eagle     DEP        0.245  0.254 0.0387    9.16    23  0.927    8.79  6.80  1.32
##  9 Green Warbler             DEP        0.363  0.467 0.0387    9.43    15  0.604    8.86  7.02  1.30
## 10 Gray Wagtail              DEP        0.425  0.253 0.136     6.52    18  2.82     6.18  5.05  1.26
## 11 Spotted Redshank          DEP        0.504  0.327 0.116     9.96    18  2.37     9.45  7.35  1.32
## 12 Tufted Duck               DEP        0.511  0.447 0.0913    7.48    13  1.31     6.96  6.28  1.15
## 13 Brown Shrike              DEP        0.519  0.282 0.134     9.55    22  3.40     9.14  6.49  1.44
## 14 Eurasian Wigeon           DEP        0.795  0.344 0.195    12.4     22  5.33    11.9   8.88  1.37
## 15 Taiga Flycatcher          DEP        0.988  0.300 0.364     8.31    19 10.9      7.91  5.59  1.45
## 16 Bar-headed Goose          DEP        1.26   0.283 0.473     9.58    22 19.7      9.17  7.31  1.28
## 17 Siberian Stonechat        DEP        1.39   0.246 0.667     5.86    16 32.1      5.52  4.50  1.26
## 18 Common Chiffchaff         DEP        1.46   0.410 0.457     8.28    15 12.6      7.78  6.10  1.31
## 19 Lesser Whitethroat        DEP        1.50   0.462 0.335    14.7     21 10.6     14.1  10.9   1.31
## 20 Red-breasted Flycatcher   DEP        1.53   0.312 0.545     9.28    20 23.9      8.85  6.69  1.36
## 21 Blyth's Reed Warbler      DEP        1.86   0.213 0.778     7.21    22 77.0      6.90  5.77  1.22
## 22 Black Redstart            DEP        2.21   0.292 0.782     6.72    16 57.3      6.34  5.27  1.24
## 23 Brown-breasted Flycatcher DEP        2.47   0.479 0.708     7.30    11 26.7      6.72  5.03  1.39
## 24 Bar-tailed Godwit         DEP        3.89   2.60  0.271    22.6      6  2.24    19.6  14.7   1.42
## 25 Cinereous Vulture         DEP        6.21   0.921 0.835    10.5      9 45.5      9.48  8.07  1.23
## 26 Blyth's Reed Warbler      ARR       -3.33   0.459 0.705    15.6     22 52.5     14.9  11.0   1.39
## 27 Cinereous Vulture         ARR       -2.39   2.38  0.101    27.1      9  1.01    24.5  17.6   1.46
## 28 Green Warbler             ARR       -1.78   0.270 0.745     5.44    15 43.8      5.11  3.92  1.34
## 29 Brown-breasted Flycatcher ARR       -1.78   1.02  0.215    15.6     11  3.02    14.4   8.60  1.74
## 30 Western Yellow Wagtail    ARR       -1.73   0.204 0.765     7.22    22 71.5      6.91  5.48  1.29
## 31 Pallid Harrier            ARR       -1.62   0.240 0.716     6.43    18 45.3      6.10  5.03  1.24
## 32 Sykes's Warbler           ARR       -1.51   0.984 0.135    21.5     15  2.34    20.2  17.3   1.20
## 33 Eurasian Wigeon           ARR       -1.35   0.272 0.527     9.81    22 24.5      9.39  7.30  1.31
## 34 Common Chiffchaff         ARR       -1.22   0.440 0.338     8.88    15  7.67     8.34  6.35  1.36
## 35 Brown-headed Gull         ARR       -1.04   0.533 0.192    14.9     16  3.80    14.1  10.6   1.36
## 36 Bar-tailed Godwit         ARR       -0.997  0.958 0.153     8.33     6  1.08     7.21  5.37  1.43
## 37 Greenish Warbler          ARR       -0.980  0.280 0.380     8.32    20 12.3      7.94  6.29  1.29
## 38 Booted Eagle              ARR       -0.976  0.209 0.548     5.38    18 21.9      5.11  3.69  1.42
## 39 Brown Shrike              ARR       -0.732  0.160 0.488     5.42    22 21.0      5.19  3.77  1.41
## 40 Taiga Flycatcher          ARR       -0.722  0.250 0.305     6.93    19  8.35     6.60  5.46  1.24
## 41 Siberian Stonechat        ARR       -0.705  0.182 0.483     4.35    16 14.9      4.10  3.04  1.39
## 42 Tufted Duck               ARR       -0.700  0.527 0.119     8.82    13  1.76     8.21  6.67  1.27
## 43 Red-breasted Flycatcher   ARR       -0.642  0.248 0.250     7.39    20  6.68     7.05  6.05  1.19
## 44 Lesser Whitethroat        ARR       -0.610  0.255 0.213     8.13    21  5.70     7.76  6.39  1.24
## 45 Black Redstart            ARR       -0.409  0.172 0.261     3.96    16  5.65     3.74  2.90  1.32
## 46 Bar-headed Goose          ARR       -0.129  0.146 0.0341    4.95    22  0.777    4.74  3.83  1.26
## 47 Greater Spotted Eagle     ARR        0.0515 0.332 0.00104  12.0     23  0.0240  11.5   8.01  1.47
## 48 Gray Wagtail              ARR        0.342  0.209 0.130     5.38    18  2.69     5.10  4.07  1.29
## 49 Common Buzzard            ARR        0.480  0.335 0.128     8.08    14  2.06     7.56  5.58  1.40
## 50 Spotted Redshank          ARR        0.552  1.02  0.0161   30.9     18  0.294   29.4  22.4   1.34

RMSE, MAE, and RSE make the most sense. Using thresholds of 20, 20, and 25 respectively, here is a summary of our example species that passed or failed wrt ARRIVAL timings.

## # A tibble: 25 × 9
##    COMMON.NAME                 SLOPE    SE   RSE  RMSE   MAE RSE.PASS RMSE.PASS MAE.PASS
##    <chr>                       <dbl> <dbl> <dbl> <dbl> <dbl> <lgl>    <lgl>     <lgl>   
##  1 Bar-headed Goose          -0.129  0.146  4.95  4.74  3.83 TRUE     TRUE      TRUE    
##  2 Bar-tailed Godwit         -0.997  0.958  8.33  7.21  5.37 TRUE     TRUE      TRUE    
##  3 Black Redstart            -0.409  0.172  3.96  3.74  2.90 TRUE     TRUE      TRUE    
##  4 Blyth's Reed Warbler      -3.33   0.459 15.6  14.9  11.0  TRUE     TRUE      TRUE    
##  5 Booted Eagle              -0.976  0.209  5.38  5.11  3.69 TRUE     TRUE      TRUE    
##  6 Brown Shrike              -0.732  0.160  5.42  5.19  3.77 TRUE     TRUE      TRUE    
##  7 Brown-breasted Flycatcher -1.78   1.02  15.6  14.4   8.60 TRUE     TRUE      TRUE    
##  8 Brown-headed Gull         -1.04   0.533 14.9  14.1  10.6  TRUE     TRUE      TRUE    
##  9 Cinereous Vulture         -2.39   2.38  27.1  24.5  17.6  FALSE    FALSE     TRUE    
## 10 Common Buzzard             0.480  0.335  8.08  7.56  5.58 TRUE     TRUE      TRUE    
## 11 Common Chiffchaff         -1.22   0.440  8.88  8.34  6.35 TRUE     TRUE      TRUE    
## 12 Eurasian Wigeon           -1.35   0.272  9.81  9.39  7.30 TRUE     TRUE      TRUE    
## 13 Gray Wagtail               0.342  0.209  5.38  5.10  4.07 TRUE     TRUE      TRUE    
## 14 Greater Spotted Eagle      0.0515 0.332 12.0  11.5   8.01 TRUE     TRUE      TRUE    
## 15 Green Warbler             -1.78   0.270  5.44  5.11  3.92 TRUE     TRUE      TRUE    
## 16 Greenish Warbler          -0.980  0.280  8.32  7.94  6.29 TRUE     TRUE      TRUE    
## 17 Lesser Whitethroat        -0.610  0.255  8.13  7.76  6.39 TRUE     TRUE      TRUE    
## 18 Pallid Harrier            -1.62   0.240  6.43  6.10  5.03 TRUE     TRUE      TRUE    
## 19 Red-breasted Flycatcher   -0.642  0.248  7.39  7.05  6.05 TRUE     TRUE      TRUE    
## 20 Siberian Stonechat        -0.705  0.182  4.35  4.10  3.04 TRUE     TRUE      TRUE    
## 21 Spotted Redshank           0.552  1.02  30.9  29.4  22.4  FALSE    FALSE     FALSE   
## 22 Sykes's Warbler           -1.51   0.984 21.5  20.2  17.3  TRUE     FALSE     TRUE    
## 23 Taiga Flycatcher          -0.722  0.250  6.93  6.60  5.46 TRUE     TRUE      TRUE    
## 24 Tufted Duck               -0.700  0.527  8.82  8.21  6.67 TRUE     TRUE      TRUE    
## 25 Western Yellow Wagtail    -1.73   0.204  7.22  6.91  5.48 TRUE     TRUE      TRUE

Figure 10: Comparisons of different measures of variability for arrival timings.

It is evident that RMSE is the most susceptible to single, large-deviance points pulling away the overall measure. It also seems that MAE might be the most appropriate for us: aside from Dunlin and Pied Harrier (which are treated similarly by all three), all other remove species have been clustered tightly and separated from the species we want to retain.

Let us check whether this is true for departure timings as well. Here, the best thresholds are 14, 10 and 15 respectively for RMSE, MAE and RSE.

## # A tibble: 25 × 9
##    COMMON.NAME                 SLOPE    SE   RSE  RMSE   MAE RSE.PASS RMSE.PASS MAE.PASS
##    <chr>                       <dbl> <dbl> <dbl> <dbl> <dbl> <lgl>    <lgl>     <lgl>   
##  1 Bar-headed Goose           1.26   0.283  9.58  9.17  7.31 TRUE     TRUE      TRUE    
##  2 Bar-tailed Godwit          3.89   2.60  22.6  19.6  14.7  FALSE    FALSE     FALSE   
##  3 Black Redstart             2.21   0.292  6.72  6.34  5.27 TRUE     TRUE      TRUE    
##  4 Blyth's Reed Warbler       1.86   0.213  7.21  6.90  5.77 TRUE     TRUE      TRUE    
##  5 Booted Eagle              -0.0444 0.250  6.45  6.12  4.95 TRUE     TRUE      TRUE    
##  6 Brown Shrike               0.519  0.282  9.55  9.14  6.49 TRUE     TRUE      TRUE    
##  7 Brown-breasted Flycatcher  2.47   0.479  7.30  6.72  5.03 TRUE     TRUE      TRUE    
##  8 Brown-headed Gull         -0.766  0.472 13.2  12.5   9.69 TRUE     TRUE      TRUE    
##  9 Cinereous Vulture          6.21   0.921 10.5   9.48  8.07 TRUE     TRUE      TRUE    
## 10 Common Buzzard            -0.272  0.880 21.2  19.9  14.1  FALSE    FALSE     FALSE   
## 11 Common Chiffchaff          1.46   0.410  8.28  7.78  6.10 TRUE     TRUE      TRUE    
## 12 Eurasian Wigeon            0.795  0.344 12.4  11.9   8.88 TRUE     TRUE      TRUE    
## 13 Gray Wagtail               0.425  0.253  6.52  6.18  5.05 TRUE     TRUE      TRUE    
## 14 Greater Spotted Eagle      0.245  0.254  9.16  8.79  6.80 TRUE     TRUE      TRUE    
## 15 Green Warbler              0.363  0.467  9.43  8.86  7.02 TRUE     TRUE      TRUE    
## 16 Greenish Warbler          -0.459  0.362 10.8  10.3   8.83 TRUE     TRUE      TRUE    
## 17 Lesser Whitethroat         1.50   0.462 14.7  14.1  10.9  TRUE     FALSE     FALSE   
## 18 Pallid Harrier             0.0227 0.334  8.96  8.50  7.00 TRUE     TRUE      TRUE    
## 19 Red-breasted Flycatcher    1.53   0.312  9.28  8.85  6.69 TRUE     TRUE      TRUE    
## 20 Siberian Stonechat         1.39   0.246  5.86  5.52  4.50 TRUE     TRUE      TRUE    
## 21 Spotted Redshank           0.504  0.327  9.96  9.45  7.35 TRUE     TRUE      TRUE    
## 22 Sykes's Warbler            0.147  0.847 18.5  17.3  13.1  FALSE    FALSE     FALSE   
## 23 Taiga Flycatcher           0.988  0.300  8.31  7.91  5.59 TRUE     TRUE      TRUE    
## 24 Tufted Duck                0.511  0.447  7.48  6.96  6.28 TRUE     TRUE      TRUE    
## 25 Western Yellow Wagtail     0.0612 0.241  8.50  8.14  6.13 TRUE     TRUE      TRUE

Figure 11: Comparisons of different measures of variability for departure timings.

RMSE seems like a poor option again. MAE is again decent, but this time RSE is also good. Need to see how values for species change with updated 2024 data.

The number of species that pass and fail each criterion are:

## # A tibble: 6 × 5
##   DATE.TYPE CRITERION  FAIL  PASS PASS.PROP
##   <fct>     <chr>     <int> <int>     <dbl>
## 1 DEP       MAE.PASS     35    55     0.611
## 2 DEP       RMSE.PASS    26    64     0.711
## 3 DEP       RSE.PASS     27    63     0.7  
## 4 ARR       MAE.PASS      7    83     0.922
## 5 ARR       RMSE.PASS    12    78     0.867
## 6 ARR       RSE.PASS      9    81     0.9

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Relationship between wintering latitude and migration synchronicity of Indian wintering birds

Karthik Thrikkadeeri

2024/08/15